Today in Pre-Calculus• Quiz until 11:20

• When you are done, turn it in and get graphing calculator (remember to leave something if you borrow one from me)

• Notes: (no handout)– Define and Identify a Continuous function– Name and Identify types of discontinuity

Homework

Continuous Functions

• Definition: A function where the graph does not come apart at any point on its domain. It is continuous everywhere on its domain.

Removable Discontinuity• This graph is continuous

everywhere except for the hole at x = 1.5

• This is called a removable discontinuity because it can be patched by redefining f(1.5) so as to plug the hole.

Removable Discontinuity• This graph also has a

removable discontinuity

• This is removable because we could define f(1.5) so as to plug the hole and make f continuous at f(1.5).

Jump Discontinuity• This discontinuity is not

removable because there is more than just a hole at x = -2.

• It is a Jump Discontinuity because there is more than a hole, there is a jump in the function values that makes it impossible to plug with a single point.

Infinite Discontinuity• This discontinuity is not

removable because there is more than just a hole at x = -1.

• It is a Infinite Discontinuity at x = -1 because the two sides are approaching infinity.

Practice

2(2 1)( )

1

xf x

x

Continuous Discontinuous-Infinite

Discontinuous-Removable

Discontinuous-Jump

DiscontinuousInfinite

Homework

• Wkst.